Hun er bange for smitte, så hun vasker sig, før hun besøger sin familie.

Yes. At være bange for is the normal Danish pattern for to be afraid of.

So you say: Hun er bange for smitte = she is afraid of infection/contagion.

It is best to learn bange for as a fixed combination. You can also use it before a clause: Hun er bange for at blive syg = she is afraid of getting sick.

Here, smitte is a noun. It means something like contagion, infection, or the spread of disease.

There is no article because Danish, like English, often uses abstract or mass nouns without one. Compare English afraid of infection.

In other sentences, at smitte can also be a verb meaning to infect or to be contagious. For example: Hun er bange for at smitte sin familie = she is afraid of infecting her family.

Because at vaske sig is a reflexive expression, meaning to wash oneself.

So: Hun vasker sig = she washes herself

The word sig shows that the subject and the object are the same person. English often does not say herself unless it needs emphasis, but Danish commonly uses the reflexive pronoun here.

Depending on context, vasker sig can mean washes herself, washes up, or sometimes something like cleans herself before going.

Sig is the third-person reflexive pronoun. You use it when the action goes back to the subject.

So: Hun vasker sig = she washes herself

But: Hun vasker hende = she washes her, meaning another female person

That is an important difference. Sig refers back to hun. Hende refers to someone else.

Because Danish uses sin/sit/sine when the owner is the same as the subject of the clause.

Here the subject is hun, and it is her own family, so: hun besøger sin familie

If you said hendes familie, it would usually mean someone else’s family or it would sound contrastive.

Also, sin is used because familie is a singular common-gender noun. If the noun were plural, you would use sine: Hun besøger sine forældre = she visits her parents

Here så means so, in the sense of therefore or as a result.

So the sentence structure is: She is afraid of contagion, so she washes herself, before she visits her family.

In other contexts, så can also mean then, but in this sentence it clearly expresses a result.

Før introduces a subordinate clause, and subordinate clauses behave differently from main clauses.

So after før, the normal order is: hun besøger sin familie

That is why you get: før hun besøger sin familie

A useful comparison is:

Hun besøger sin familie.
This is a main clause.

Før hun besøger sin familie, vasker hun sig.
Now før hun besøger sin familie is a subordinate clause, and the main clause after it becomes vasker hun sig.

No. At besøge takes a direct object.

So you say: besøge sin familie besøge en ven besøge sin bedstemor

You do not need a preposition here. In that way, it works a lot like English visit someone.

Danish normally repeats the subject in each clause. It does not usually drop subject pronouns the way some other languages do.

So this is natural: Hun er bange for smitte, så hun vasker sig, før hun besøger sin familie.

Leaving out one of the hun forms would sound ungrammatical or very unnatural.

The commas help separate the clauses.

The first comma, before så, separates two main clauses: Hun er bange for smitte, så hun vasker sig ...

The second comma, before før, marks the start of the subordinate clause: ..., før hun besøger sin familie.

In Danish, the comma before a subordinate clause can depend on the comma system being used. Many learners will see this comma written, and it is perfectly normal here.